If three successive discounts of 20%, 30% and 40% are given, then what will be the net discount (in per cent) ?

Options

A. 80
B. 87.6
C. 90
D. 66.4

Answer

To find the net discount after three successive discounts of 20%, 30%, and 40%, we can use two methods. Here, I will provide a step-by-step solution using both methods.

### Method 1: Using the Formula for Successive Discounts

1. **Calculate the first two discounts (20% and 30%)**:
- Let the first discount be \( x = 20\% \) and the second discount be \( y = 30\% \).
- Using the formula for two successive discounts:
\[ \text{Net Discount} = x + y - \frac{x \cdot y}{100} \]
- Substitute the values:
\[ \text{Net Discount} = 20 + 30 - \frac{20 \cdot 30}{100} \]
- Calculate:
\[ = 50 - 6 = 44\% \]

2. **Now, include the third discount (40%)**:
- Let the net discount from the first two discounts be \( z = 44\% \).
- Now, apply the third discount:
\[ \text{Final Net Discount} = z + 40 - \frac{z \cdot 40}{100} \]
- Substitute the value of \( z \):
\[ = 44 + 40 - \frac{44 \cdot 40}{100} \]
- Calculate:
\[ = 84 - 17.6 = 66.4\% \]

### Method 2: Calculating the Remaining Price After Each Discount

1. **Start with the original price (assume 100)**:
- After the first discount of 20%:
\[ \text{Price after 20%} = 100 - 20 = 80 \]

2. **Apply the second discount of 30% on the new price**:
- After the second discount:
\[ \text{Price after 30%} = 80 - 30\% \text{ of } 80 = 80 - 24 = 56 \]

3. **Apply the third discount of 40% on the new price**:
- After the third discount:
\[ \text{Price after 40%} = 56 - 40\% \text{ of } 56 = 56 - 22.4 = 33.6 \]

4. **Calculate the total discount**:
- The total discount from the original price of 100 is:
\[ \text{Total Discount} = 100 - 33.6 = 66.4\% \]

### Final Answer
The net discount after three successive discounts of 20%, 30%, and 40% is **66.4%**.